Question

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

• A. Only (i) can correspond to the unfolded cube in Panel I.
• B. Only (ii) can correspond to the unfolded cube in Panel I.
• C. Both (i) and (ii) can correspond to the unfolded cube in Panel I.
• D. Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.

Hint:

Label each square of the net as a face of the cube, remember opposite faces never appear together in one view, then trace where the shaded corner lands after folding.

Answer 1

The Correct Option is B

Step 1: Label every square of the net as a face of the cube.
Read Panel I as a vertical strip of four squares with one square attached on the left and one on the right of the second square from the top.
Call the top square Top, the square below it Front, the two side squares Left and Right, the next square down Bottom, and the last square at the very bottom Back.
This matches how a plus shaped net always folds up, the two squares that flank the middle square become the Left and Right faces, and the strip above and below the middle square become Top, Bottom and finally Back.

Step 2: Note which faces can never appear together.
When six faces close up into a cube, each face has exactly one face directly opposite it, Top is opposite Bottom, Front is opposite Back, and Left is opposite Right.
Any single 3D view of a cube can only show three faces that all meet at one corner, so it can never show a face together with its own opposite face.

Step 3: Read off the shading from the net.
The Left and Right squares in Panel I are both fully shaded dark.
The Top square carries a gray triangle cut across one of its corners, and the Back square carries a gray patch across part of it, while the Front and Bottom squares are left plain white.

Step 4: Trace the shaded corner of the Top square through the fold.
The edge of the Top square that is joined to the Front square becomes the Top-Front edge of the cube once folded.
Because the shaded triangle sits on the far corner of the Top square, away from that joining edge, it lands on the corner of the cube shared by the Top face, the Back face and one of the side faces, not on the Top-Front corner.
So on the finished cube, any view that shows the shaded triangle sitting right next to the Front face, at the near corner of the Top face, is not consistent with the net.

Step 5: Compare with cube (i) and cube (ii).
In cube (i), the shaded triangle on the Top face is drawn touching the near, front corner of the top face, the same corner where the visible side face meets the front edge. That placement contradicts the tracing done in Step 4, so cube (i) cannot be folded from this net.
In cube (ii), the shaded triangle on the Top face sits on the far corner, away from the front edge, exactly where Step 4 places it, and the fully shaded side face matches the Left or Right square of the net. This is consistent in every corner and every shaded region.

Final Answer:
Only cube (ii) can be produced by folding the net in Panel I.
\[ \boxed{\text{Only (ii)}} \]